A posteriori error estimation and anisotropic mesh adaptation in
3-D compressible flow simulations

Yves Bourgault
Department of Mathematics and Statistics
University of Ottawa


Anisotropic mesh adaptation has proved to be a powerful strategy to
improve the quality and efficiency of finite element/volume methods.
These anisotropic mesh adaptation techniques were initially based on
a metric derived from a numerical approximation of the Hessian of the
solutions with, in the background, the use of a priori error
estimates. More recently, anisotropic a posteriori error estimators
were derived and used to drive anisotropic mesh adaptation. These a
posteriori estimators are well developed for elliptic and parabolic
equations, such as the Navier-Stokes equations, but few works address
their efficiency at computing inviscid flows. We will present adapted
meshes and solutions for 3-D inviscid flows around a supersonic
aircraft, as obtained with an anisotropic a posteriori estimator.
Compressible flows are computed using a vertex-centred finite volume
method. The anisotropic adapted meshes are obtained in a
solver/mesher loop with a mesh adaptation software implementing local
mesh modification techniques. We will also compare our solutions with
those obtained with the most recent a priori error estimators. The
goal of the project is to develop simulation capabilities for complex
3-D external flows that run on simple desktops in a limited time and
with limited memory.